Incidence of q statistics in rank distributions.
Saved in:
| Title: | Incidence of q statistics in rank distributions. |
|---|---|
| Authors: | Yalcin, G. Cigdem1, Robledo, Alberto2, Gell-Mann, Murray3 mgm@santafe.edu |
| Source: | Proceedings of the National Academy of Sciences of the United States of America. 9/30/2014, Vol. 111 Issue 39, p14082-14087. 6p. |
| Subjects: | Lyapunov exponents, Numerical solutions to differential equations, Bifurcation theory, Stability (Mechanics), Entropy |
| Abstract: | We show that size-rank distributions with power-law decay (often only over a limited extent) observed in a vast number of instances in a widespread family of systems obey Tsallis statistics. The theoretical framework for these distributions is analogous to that of a nonlinear iterated map near a tangent bifurcation for which the Lyapunov exponent is negligible or vanishes. The relevant statistical-mechanical expressions associated with these distributions are derived from a maximum entropy principle with the use of two different constraints, and the resulting duality of entropy indexes is seen to portray physically relevant information. Whereas the value of the index α fixes the distribution's power-law exponent, that for the dual index 2 - α ensures the extensivity of the deformed entropy. [ABSTRACT FROM AUTHOR] |
| Copyright of Proceedings of the National Academy of Sciences of the United States of America is the property of National Academy of Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
|---|---|
| Header | DbId: egs DbLabel: Engineering Source An: 98788415 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: Incidence of q statistics in rank distributions. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Yalcin%2C+G%2E+Cigdem%22">Yalcin, G. Cigdem</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Robledo%2C+Alberto%22">Robledo, Alberto</searchLink><relatesTo>2</relatesTo><br /><searchLink fieldCode="AR" term="%22Gell-Mann%2C+Murray%22">Gell-Mann, Murray</searchLink><relatesTo>3</relatesTo><i> mgm@santafe.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Proceedings+of+the+National+Academy+of+Sciences+of+the+United+States+of+America%22">Proceedings of the National Academy of Sciences of the United States of America</searchLink>. 9/30/2014, Vol. 111 Issue 39, p14082-14087. 6p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Lyapunov+exponents%22">Lyapunov exponents</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+solutions+to+differential+equations%22">Numerical solutions to differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Bifurcation+theory%22">Bifurcation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Stability+%28Mechanics%29%22">Stability (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Entropy%22">Entropy</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We show that size-rank distributions with power-law decay (often only over a limited extent) observed in a vast number of instances in a widespread family of systems obey Tsallis statistics. The theoretical framework for these distributions is analogous to that of a nonlinear iterated map near a tangent bifurcation for which the Lyapunov exponent is negligible or vanishes. The relevant statistical-mechanical expressions associated with these distributions are derived from a maximum entropy principle with the use of two different constraints, and the resulting duality of entropy indexes is seen to portray physically relevant information. Whereas the value of the index α fixes the distribution's power-law exponent, that for the dual index 2 - α ensures the extensivity of the deformed entropy. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Proceedings of the National Academy of Sciences of the United States of America is the property of National Academy of Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=98788415 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1073/pnas.1412093111 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 6 StartPage: 14082 Subjects: – SubjectFull: Lyapunov exponents Type: general – SubjectFull: Numerical solutions to differential equations Type: general – SubjectFull: Bifurcation theory Type: general – SubjectFull: Stability (Mechanics) Type: general – SubjectFull: Entropy Type: general Titles: – TitleFull: Incidence of q statistics in rank distributions. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Yalcin, G. Cigdem – PersonEntity: Name: NameFull: Robledo, Alberto – PersonEntity: Name: NameFull: Gell-Mann, Murray IsPartOfRelationships: – BibEntity: Dates: – D: 30 M: 09 Text: 9/30/2014 Type: published Y: 2014 Identifiers: – Type: issn-print Value: 00278424 Numbering: – Type: volume Value: 111 – Type: issue Value: 39 Titles: – TitleFull: Proceedings of the National Academy of Sciences of the United States of America Type: main |
| ResultId | 1 |
